The president takes precedence. But first we are overshooting the runway coming into Mexico City in a storm. We are down to a few hundred feet when we suddenly swerve and shoot almost straight in the air. I want to brace but am thrown on my back like a beetle. The wings shudder, the passengers are wild-eyed, the stewardess is white-faced with panic. The plane sounds like it is nearing the end of its life. I am worried I am, too. The woman in the next seat turns to me and says: “I am going to puke!” This is it, I think. We might not make it. We may be going to die.

A gut-churning hour and a half later we are finally skidding back into land. The mountains are bleak, the sky black, the runway is awash with water. We slew before we stop. When we finally crawl off the plane, Enrique Olvera is waiting. “It would be a good death,” he grins. “Fast. It’d only take a minute.” I think about being skewered by fuselage and say I’ll meet him at his restaurant Pujol in a couple of hours. I need to rediscover my stomach, get my appetite back. I have been looking forward to this meal for five years.

Olvera was 12 hours late when we met in Oaxaca [pronounced Wahaca] the day before. The president of Mexico, Enrique Peña Nieto, had asked him to speak at the launch of an initiative to build tourism based around food. Olvera is the face of modern Mexican cooking, the high-profile chef with the highest rated restaurants. For his speech, though, he attacked government lack of strategy on biodiversity, GMOs and conditions in the food and farming industries.

“I can do conferences, congresses, but I was very nervous,” he says. “I was in front of the president, 10 governors, the secretary. There was a lot of business people, the richest in Mexico, from the big food and brewing companies. I was going to give them shit. I was going to give shit to the president. The head of one of the largest businesses became upset when I told him he was poisoning my pumpkins.”

We are in Oaxaca to meet Luis Arellano. As often with Olvera, there is much laughter, intense talk, good eating, many bottles of mezcal. The next morning we drive to the Mercado de Villa de Etla. Finding good food is a full-time job at Pujol.

“I cannot use 90 per cent of the food that is easily available to me,” says Olvera. “High-quality sustainable meat is hard to get in Mexico, there is still no pride in raising livestock so we depend on smaller animals: pig, sheep and goats. I have Luis on the payroll as a sous chef at Pujol yet he lives here in Oaxaca. His only role is to get us the best produce available. He goes to the purveyors, talks to the producers. I have a full-time person finding stuff for me so I can get my hands on the best corn and chillies; to find a fish-seller. It is hard.”

The quality of the produce in the market is high, sold by farmers from the fertile valleys around the town. We pass the crunchy grasshopper vendor (best eaten in early summer when they are small, says Olvera) through exotic cheese, chilli, fruit and vegetable stalls before stopping for a bowl of tripe soup. Spiked with coriander, onions, garlic, lime and chilli, the broth is delicious though the tripe bobs like body parts and is as thick as my thumb. When Olvera declares it hasn’t been thoroughly cleaned I feel absolved to leave it alone.

I first met Olvera at the one of the final meals at Ferran Adrià’s El Bulli, in Catalonia, northern Spain. We shared a table. He is a good dinner companion: opinionated, smart and serious about food without taking himself too seriously. The last time I saw him was in Copenhagen for René Redzepi’s MAD Camp. Redzepi is a friend. “I’ve spent a holiday with him in Oaxaca,” the Noma chef says via email, “just me and him in a house. Our families did a New Year’s Eve vacation and we have shared many a mezcal over the years.

“Since then I’ve fallen in love with Mexican food and its culture,” he writes. “I spend a month there every year. He’s one of the guys that I look up to in terms of his whole life and work balance: he has a way of mixing perfect doses of ‘let’s take it easy, I don’t give a fuck’ and total seriousness and dedication.”

Olvera’s drive and dedication took him to New York late last year, his first restaurant venture outside Mexico. His place Cosme opened to great reviews including three stars from Pete Wells at the New York Times. “I was very rigorous when we opened,” says Olvera. “I ate at a lot of places, talked to a lot of people. We made a commitment that I would stay there six months straight, people understood that.

“In New York I am cooking with purple asparagus, kohlrabi, what is good and what is available. I can make these things taste Mexican. We never expected the success, the warm welcome. When the reviews were good, customers sent flowers. Other chefs were amazing. I feel like a Mexican New Yorker. I wear a Yankees cap now.”

Our next Mexican stop is the farm of Macedonia Garcia, outside Oaxaca, where they still also use the milpa system. Here the pre-Hispanic “three sisters” are sown together: squash providing ground cover, beans to climb up growing corn. But this is corn like none you may ever find outside Mexico, huge cobs bejewelled with different colours; heritage grain grown in rust-soiled fields. The Mayan creation legend says man was born from corn and here it is almost easy to believe. It is the backbone of all Mexican cooking, says Olvera, the foodstuff everyone eats: the four Ts – tacos, tamales, tortas, tortillas. “Street food is where 80% of Mexicans eat,” says Olvera, “from the market or on the street. Other dining lacks that potency. With street food the flavours are strong. What we had when we were kids.”

Mexican corn can become an obsession, I find myself constantly sniffing and smelling tacos and tortillas, recognising the subtle differences in grain, smoke and seasoning. In the end I don’t much care what’s served with it. It is the corn that is the thing.

Isaac McHale, head chef at London’s Clove Club, is another fan, serving a taco inspired by a recent visit to Pujol. “It took me a while to realise the flavour of Mexico was the corn,” he says. “People thought Enrique was mad when he served tacos at first, but he was just doing something true to himself. Small production corn gently cooked into beautiful vehicles. It isn’t just a way to hold a variety of meats and cactus. The flavour of the corn is the most important of all, the one that stays with you after everything else is gone.”

Next, Luis takes us to the holy grail of grain: Oaxacan home of Elvia León Hernández, mother of Jorge who makes the mole [prononunced molay], the essential sauce at the centre of Mexican cooking, for Pujol. Multicoloured corns and their pastes are laid out for us while Senora Hernández makes tortillas on a wide shallow pan over burning wood. A black mole is bubbling in a pot over fire outside. Two fat pigs are grunting happily opposite. Smiling curious children run around. The farmer comes to shake our hand. We eat extraordinary tortillas with guacamole and tomato salsa; blue quesadillas stuffed with Oaxacan cheese. We savour complex flavours in different colours, wipe clean plates of mole. We feast like corn farmers and kings.

Back in the capital, I ask Mexican chef Oswaldo Oliva, formerly of Mugaritz, about Olvera’s place in his country’s food culture. “Enrique was able to look beyond traditional cooking at a time when no one else did,” he says. “Fine dining was tainted with Frenchness. Diversity was hard to find. For many years he has been putting the brand ‘Mexico’ out there. He has been the leader nobody wanted but everybody needed.”

And so to Pujol. The moment I walk in the door I relax. The room is loud and dark. A large red octopus like a sailor’s tattoo is on one wall. Furniture is Danish-style mid-century, carefully chosen. The staff are in black and the right sort of invisible. The food comes in an immaculate procession of precise plates.

“When we opened we just wanted to do a nice neighbourhood restaurant,” says Olvera. “The first few years we were focused on not closing. We still are. I went to culinary school in New York so new American cuisine – Alice Waters, Thomas Keller – were my influences and it showed in the cooking. We didn’t have tarragon we had cilantro but our technique was classic French.

“As time progressed we realised flavour is the most important thing. We cooked from memory and soul. Pujol was the first contemporary Mexican restaurant. Before us there was nothing. I don’t want to be the most creative restaurant. I want to be the most delicious. I want to make you remember with a smile on your face.”

For the next few hours, the bass is heavy, the beat insistent, the laughter and conversation loud. The theatre of food unfolds. “As I grow older I have grown out of fine dining,” says Olvera. “The older I get the less I like it. I like to play the music loud. I like it when people misbehave. As long as they don’t dance on the tables, but everything else …”

The menu is structured as if you are being entertained at home: tequila and canapes followed by smoke and char from coal and corn. The meal is a masterclass of sophisticated tamales, tostadas, a stunning suckling lamb taco. The mother mole is served with a freshly made mole in the centre. Both shine with skill. Flavours are bitter, spicy, sour, smoky, earthy, like Mexico. But this isn’t Tex-Mex and mariachi. This is the Mexico of poets, architects and painters: of Octavio Paz, Luis Barragán, Frida Kahlo, Diego Rivera, and of Enrique Olvera.

“If you build on your grandmother’s recipe, the taco stand you visited as a kid, that is when you are most successful,” he says. “It is a modern idea to do the food of your childhood. Having a taco, I know that is right and wrong. I know what it needs. If I do pasta I probably wouldn’t be exceptional. They say Mexicans don’t have identity, they have history. We are a mix of many cultures.”

The next day, my last, I go to see the Diego Rivera murals at the Palacio Nacionale. There among the giant paintings of conquistadors, corrupt priests and politicians are Mayan farmers growing corn like Macedonia Garcia. I remember my meal at Pujol and smile just as Olvera wanted. A brilliant menu from a brilliant cook. The highlight? The green taco with chile poblano. It is perfect. To die for, of course.

Mexico from the Inside Out by Enrique Olvera, published by Phaidon, £39.95. Click here to order a copy for £31.96 from the Guardian Bookshop

In search of a perfect taco

Writing in his new book, Mexico from the Inside Out, published by Phaidon this month, Enrique Olvera explains his country’s tortilla obsession

Street food has particularly strong roots in Mexico City, where over 10 million people use public transportation daily. Held hostage by traffic, hungry commuters satisfy their cravings on the sidewalk. Juan Villoro [Mexican journalist and author] says that nomadic and vagrant cuisine feeds people not where hunger leads them but where traffic drops them off.

We also eat on the street for pleasure, free from social class distinction. Even the highest-ranking executive shamelessly wolfs down a taco.

Parts of my memories are wrapped in tortillas: tacos de cabeza in Monterrey; tacos de langosta in Puerto Nuevo; tacos de lechon in Mérida; tacos de hoja santa in Oaxaca; tacos de carnitas con chicharrón, de bistec, or al pastor in Mexico City. No two are the same.

We eat tacos practically every day, and while they look like ordinary street food, they are anything but that. They sum up what, and how, we like to eat. Since 2008, I’ve delved into the taco’s form and taken it from the streets to Pujol. When people complained that the best tacos are on the streets, not in restaurants, we committed to provide them with something more complex, and delicious than what they have eaten before.

To make a better taco, we first had to make a better tortilla. I asked chef Luis Arellano to do whatever it took to produce the perfect tortilla. At first he thought I was joking: people think that making tortillas is simple, but it’s not; and the task turned into an obsession.

We started with sourcing the best ingredients. We tested around twenty varieties of corn – white, yellow, purple, red, and blue – until we found which was best for each recipe.

We nixtamalized [process for preparing corn] with slaked lime until we got elegant texture. We bought a small metal mill, assuming it was the eighth wonder of the world, but it was useless. Finally, we found a supplier with a stone mill.

We then tried to make our own masa. Kneaded with water, it should be soft and compact, and shouldn’t stick to your hands or break and fall apart.

The tortilla has an irregular form; its edges are naturally wavy. With a wooden press, we experimented until we found the right amount of dough for a flat, uniform tortilla, not too thick and not too fragile.

We deduced the exact number of seconds a tortilla should fry in a comal to become the platonic ideal we were after.

We still keep samples of the corn at the restaurant that constituted the beginning of this story – a reminder of our excitement when we had to defend each time we prepared tacos and served tortillas, instead of bread, in Pujol.

Today we are using fewer varieties of corn than when we began: changing them according to the dishes, seasons, and access to the grain. Since 2014, after we found a machine that fit in the kitchen, we’ve been milling our own corn at Pujol.

At Pujol, we don’t see the tortilla as a mere base for the taco, but as edible tableware, tailoring the tortillas to what we will top them with.

Extracted from Mexico from the Inside Out by Enrique Olvera, published by Phaidon. Olvera will host a supper club in London, as part of Wahaca’s Day of the Dead festival; wahaca.co.uk/dotd/supper-club